14.7 Antiparticles and Radioactive Decay

Introduction

The concepts of antiparticles and radioactive decay are central to our understanding of the subatomic world. Antiparticles represent a fundamental symmetry in nature, while radioactive decay processes like alpha and beta decay reveal the mechanisms by which unstable atomic nuclei transform to achieve stability.

Antiparticles

For every type of fundamental particle, there exists a corresponding antiparticle. An antiparticle has the same mass and spin as its particle counterpart but has an opposite electric charge and other quantum numbers.

• Discovery: The existence of antiparticles was first predicted by Paul Dirac in 1928 and confirmed with the discovery of the positron in 1932.
• Annihilation: When a particle and its antiparticle meet, they can annihilate each other, converting their entire mass into energy, typically in the form of high-energy photons (gamma rays), according to $E=m{c}^2$.

Examples of Particle-Antiparticle Pairs

Beta (β) Decay

Beta decay is a type of radioactive decay in which a beta particle (a high-energy electron or positron) is emitted from an atomic nucleus. This process is mediated by the weak nuclear force and allows an unstable nucleus to get closer to the optimal neutron-to-proton ratio for stability.

a) Beta-Minus (β⁻) Decay

In nuclei with an excess of neutrons, a neutron is converted into a proton.

• Process: A neutron transforms into a proton, an electron (the β⁻ particle), and an electron antineutrino.
• Equation: $n\to p^{+}+e^{-}+{\bar{\nu }}_e$
• Effect on the Nucleus:
  • The number of neutrons decreases by 1.
  • The number of protons increases by 1.
  • The atomic number (Z) increases by 1, changing the element.
  • The mass number (A) remains unchanged.

b) Beta-Plus (β⁺) Decay (Positron Emission)

In nuclei with an excess of protons, a proton is converted into a neutron.

• Process: A proton transforms into a neutron, a positron (the β⁺ particle), and an electron neutrino.
• Equation: $p^{+}\to n+e^{+}+{\nu }_e$
• Effect on the Nucleus:
  • The number of protons decreases by 1.
  • The number of neutrons increases by 1.
  • The atomic number (Z) decreases by 1, changing the element.
  • The mass number (A) remains unchanged.

Quark-Level Description of Beta Decay

At the most fundamental level, beta decay is a transformation of one type of quark into another, mediated by the weak nuclear force (via $W$ bosons).

β⁻ Decay at the Quark Level

A neutron has quark composition $udd$ and a proton has quark composition $uud$. In ${\beta }^{-}$ decay:

$d\to u+e^{-}+{\bar{\nu }}_e$

A down quark ($d$, charge $-\frac{1}{3}e$) converts into an up quark ($u$, charge $+\frac{2}{3}e$). This changes the neutron ($udd$) into a proton ($uud$), increasing Z by 1.

β⁺ Decay at the Quark Level

In ${\beta }^{+}$ decay, an up quark converts into a down quark:

$u\to d+e^{+}+{\nu }_e$

This changes a proton ($uud$) into a neutron ($udd$), decreasing Z by 1.

Energy Spectra of Alpha and Beta Decay

The energy of the particles emitted during radioactive decay reveals important information about the process.

a) Alpha (α) Decay: Discrete Energy Spectrum

• Process: An alpha particle (a helium nucleus, ${}_2^4\text{He}$) is emitted from the parent nucleus.
• Composition: 2 protons + 2 neutrons; charge $+2e$; mass $\approx 6.64\times 10^{-27}$ kg.
• Energy: Because there are only two products (alpha particle + daughter nucleus), conservation of energy and momentum dictates that the alpha particle is emitted with a specific, discrete kinetic energy for a given decay.
• Reason: Nuclear energy levels are quantized. The decay is a transition between two fixed energy levels, so the released energy is always the same.

b) Beta (β) Decay: Continuous Energy Spectrum

• Energy: Unlike alpha particles, the electrons or positrons emitted in beta decay have a continuous range of kinetic energies, from nearly zero up to a maximum value.
• Reason — The Neutrino's Role: Beta decay is a three-body process: the decay energy is shared among the daughter nucleus, the beta particle, and the neutrino (or antineutrino). This energy can be distributed in a nearly infinite number of ways, producing a continuous energy spectrum for the beta particle.
• Historical significance: The continuous spectrum was a major puzzle until Wolfgang Pauli proposed the existence of the neutrino in 1930 to account for the missing energy.

Summary

• Antiparticles: Same mass as particle counterpart, but opposite charge and quantum numbers.
• Beta decay at quark level: ${\beta }^{-}$ involves $d\to u$; ${\beta }^{+}$ involves $u\to d$.
• Energy spectra: Alpha decay (two-body) → discrete energy; Beta decay (three-body, includes neutrino) → continuous energy.

Applications: PET scans (positron emission), nuclear medicine, fundamental particle physics research.